The objective of this protocol is to determine a safe dose of a 21-day continuous infusion of topotecan administered to children with relapsed solid tumors and no bone marrow involvement. This dose will then be used in a phase-II trial in children with relapsed leukemia and possibly in children with relapsed solid tumors. If active in leukemia as a single agent, topotecan will probably have its major use in maintenance therapy. Severe myelosuppression should be avoided during maintenance treatment. Therefore, the pediatric MTD must be found in patients without bone marrow disease. This MTD would allow future studies of this schedule in children with leukemia or solid tumors.